# Taylor formula for distributions

• Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1988

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## Abstract

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CONTENTS0. Introduction................................................................................................................................................................51. Preliminary remarks...................................................................................................................................................62. Hyperfunctions and their generalizations.................................................................................................................103. Flat functions; definitions and properties.................................................................................................................144. Taylor formula for quasi $O\left({x}^{a}\right)$ functions.............................................................................................................185. Homogeneous distributions and their properties......................................................................................................206. Mellin transformable distributions.............................................................................................................................227. Differential equations in the space of Mellin transformable distributions. Operational calculus for ℳ......................268. Taylor formula for distributions.................................................................................................................................299. Taylor transformation for functions and distributions................................................................................................3210. Spectral support of a function and of a distribution................................................................................................3311. Determination of singularities of solutions of ordinary linear differential operators with smooth coefficients..........3611. 1. Asymptotic expansion of the push-forward operation ${F}_{\ast }\phi$ for F admitting an F-invariant operator...........4012. Value of a function (distribution) at a point.............................................................................................................4113. Taylor formula for the product of functions.............................................................................................................4414. Multiplication of distributions. Taylor formula for the product of distributions..........................................................4714.1. Spectral topology................................................................................................................................................5014.2. Heuristic remarks concerning multiplication of distributions.................................................................................5114.3. Taylor formula for the function 1/f........................................................................................................................5115. Taylor formula for composite functions...................................................................................................................52References ..................................................................................................................................................................56

## How to cite

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Bogdan Ziemian. Taylor formula for distributions. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1988. <http://eudml.org/doc/268619>.

@book{BogdanZiemian1988,
abstract = {CONTENTS0. Introduction................................................................................................................................................................51. Preliminary remarks...................................................................................................................................................62. Hyperfunctions and their generalizations.................................................................................................................103. Flat functions; definitions and properties.................................................................................................................144. Taylor formula for quasi $O(x^a)$ functions.............................................................................................................185. Homogeneous distributions and their properties......................................................................................................206. Mellin transformable distributions.............................................................................................................................227. Differential equations in the space of Mellin transformable distributions. Operational calculus for ℳ......................268. Taylor formula for distributions.................................................................................................................................299. Taylor transformation for functions and distributions................................................................................................3210. Spectral support of a function and of a distribution................................................................................................3311. Determination of singularities of solutions of ordinary linear differential operators with smooth coefficients..........3611. 1. Asymptotic expansion of the push-forward operation $F_\{∗\}φ$ for F admitting an F-invariant operator...........4012. Value of a function (distribution) at a point.............................................................................................................4113. Taylor formula for the product of functions.............................................................................................................4414. Multiplication of distributions. Taylor formula for the product of distributions..........................................................4714.1. Spectral topology................................................................................................................................................5014.2. Heuristic remarks concerning multiplication of distributions.................................................................................5114.3. Taylor formula for the function 1/f........................................................................................................................5115. Taylor formula for composite functions...................................................................................................................52References ..................................................................................................................................................................56},
author = {Bogdan Ziemian},
keywords = {spectral product of distributions; Taylor transform; spectral; support; Mellin transform; Taylor development of distributions},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Taylor formula for distributions},
url = {http://eudml.org/doc/268619},
year = {1988},
}

TY - BOOK
AU - Bogdan Ziemian
TI - Taylor formula for distributions
PY - 1988
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTS0. Introduction................................................................................................................................................................51. Preliminary remarks...................................................................................................................................................62. Hyperfunctions and their generalizations.................................................................................................................103. Flat functions; definitions and properties.................................................................................................................144. Taylor formula for quasi $O(x^a)$ functions.............................................................................................................185. Homogeneous distributions and their properties......................................................................................................206. Mellin transformable distributions.............................................................................................................................227. Differential equations in the space of Mellin transformable distributions. Operational calculus for ℳ......................268. Taylor formula for distributions.................................................................................................................................299. Taylor transformation for functions and distributions................................................................................................3210. Spectral support of a function and of a distribution................................................................................................3311. Determination of singularities of solutions of ordinary linear differential operators with smooth coefficients..........3611. 1. Asymptotic expansion of the push-forward operation $F_{∗}φ$ for F admitting an F-invariant operator...........4012. Value of a function (distribution) at a point.............................................................................................................4113. Taylor formula for the product of functions.............................................................................................................4414. Multiplication of distributions. Taylor formula for the product of distributions..........................................................4714.1. Spectral topology................................................................................................................................................5014.2. Heuristic remarks concerning multiplication of distributions.................................................................................5114.3. Taylor formula for the function 1/f........................................................................................................................5115. Taylor formula for composite functions...................................................................................................................52References ..................................................................................................................................................................56
LA - eng
KW - spectral product of distributions; Taylor transform; spectral; support; Mellin transform; Taylor development of distributions
UR - http://eudml.org/doc/268619
ER -

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